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  1. On potential embedding and versions of Martin's axiom.Sakaé Fuchino - 1992 - Notre Dame Journal of Formal Logic 33 (4):481-492.
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  • Some remarks on openly generated Boolean algebras.Sakaé Fuchino - 1994 - Journal of Symbolic Logic 59 (1):302-310.
    A Boolean algebra B is said to be openly generated if {A: A ≤rc B, |A| = ℵ0} includes a club subset of [ B]ℵ0 . We show: (V = L). For any cardinal κ there exists an L∞κ-free Boolean algebra which is not openly generated (Proposition 4.1). (MA+(σ-closed)). Every L∞ℵa -free Boolean algebra is openly generated (Theorem 4.2). The last assertion follows from a characterization of openly generated Boolean algebras under MA+(σ-closed) (Theorem 3.1). Using this characterization we also prove (...)
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  • The Trend of Logic and Foundation of Mathematics in Japan in 1991 to 1996.Yuzuru Kakuda, Kanji Namba & Nobuyoshi Motohashi - 1997 - Annals of the Japan Association for Philosophy of Science 9 (2):95-110.
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  • Partial orderings with the weak Freese-Nation property.Sakaé Fuchino, Sabine Koppelberg & Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (1):35-54.
    A partial ordering P is said to have the weak Freese-Nation property if there is a mapping tf : P → [P]0 such that, for any a, b ε P, if a b then there exists c ε tf∩tf such that a c b. In this note, we study the WFN and some of its generalizations. Some features of the class of Boolean algebras with the WFN seem to be quite sensitive to additional axioms of set theory: e.g. under CH, (...)
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